The Glory of philosophy: An Exoneration of Inductive Inference



The Glory of Philosophy: An Exoneration of Inductive Inference

ABSTRACT

At the very root of his critique of inductive inference, Hume unwittingly employed inductive inference. Hence his entire critical analysis suffers from the same defects he believed all induction suffers. Though Hume was correct when he declared that “custom” plays a fundamental role in inductive inferences, this applies only to the process of human thinking. However, the ideational content involved in all inductive inference is not established by mere custom but is selected according to objective and logical standards of judgment. With regard to the relations between cause and effect, Hume concluded these relations exists only in our mind. In so doing, he was focused too closely on the subjective or psychological side of things and failed to take into account the physical dynamic that objectively exists between causal conditions and their subsequent effects state. It is the physical existence of a dynamic, or energy-link, between a cause and its effect that differentiates causality from coincidence. Finally, I show that extreme skepticism falls by its own sword because it implicitly makes use of a presumed supra-human perspective.

The Glory of Philosophy: An Exoneration of Inductive Inference

It is well known that in the throes of Europe’s scientific revolution of the 14th century Francis Bacon sketched out the philosophical foundations of the newly emerging empirical sciences in his 1620 paean to inductive inference: Novum Organum.[i] Thereafter, for well over one hundred years, scientists and philosophers worked hand in glove in the belief that the new edifice of empirical knowledge they were raising was mounted upon a secure foundation.

Then came David Hume.

In his An Enquiry Concerning Human Understanding, Hume created a doctrine that cast grave doubt upon our ability to rely on inductive inferences. Although Hume personally advocated a “mitigated skepticism”[ii], his criticisms not only tended to pull the rug out from under the new and rapidly expanding physical sciences, they also threw a cloak of insecurity over a vast area of human claims to reliable knowledge about the physical world.[iii]

Now as most everyone admits (including Hume[iv]), on a pragmatic level inductive inference works.[v] Accordingly, the workaday world has gone on much as though Hume never existed. But in philosophy his probing cut a wide swath. It is not that thinkers have been persuaded to abandon induction, so much as the inability to validate its virtues has continued to rankle in the philosophical breast. Over the years a host of writers have taken up this challenge[vi], with counter claims ranging from apriorism,[vii] “hardwired” thinking[viii], “self-supporting” arguments[ix], and stratagems to “evade”[x] the problem, to assertions that “there is no problem”[xi] and the whole issue is “fictitious”.[xii] Unfortunately, though most counter claims do make a valid point, none have succeeded in putting the specter of skepticism to rout, and the lament C. D. Broad voiced on the tercentenary of Bacon’s death remains yet: “May we venture to hope that when Bacon’s next centenary is celebrated the great work which he set going will be completed; and that Inductive reasoning, which has long been the glory of Science, will have ceased to be the scandal of philosophy”.[xiii]

Though it might appear all avenues have been exhausted in this matter and the field conceded to Hume, in fact that is not the case. I here offer a new and untried approach, one that is able to fully exonerate inductive inference and reassert the glory that (supposedly) prevailed in the philosophy of science from the time of Francis Bacon to the days of Hume.

First, a few brief and well-worn quotations from Hume will set out his position.

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain… Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise.[xiv]

In response, it has been argued that, because “nature is uniform”[xv] it is only reasonable to infer the sun will rise tomorrow just as it has always risen in the past. But Hume had anticipated this response.

All inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded upon the supposition of that resemblance.[xvi]

Others have claimed that, although predicting the future with complete certainty may be beyond us, we are still able to make probability predictions. In practice this is true. However, arguments advocating a probability approach do not address Hume’s philosophical concern. That is, if we wish to make a probability statement about the future, whether we base that statement upon the “frequency”[xvii] of past events or appeal to our level of “belief”[xviii], we must first assume the information we are using is in some way relevant to future events. But Hume’s concern was: how do we know any information we have is relevant to future events? Probability arguments, in his view, succumb to the same circular reasoning as other justifications of induction.

All our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.[xix]

According to Hume, all attempts at justifying induction beg the question. Furthermore, logic is unable to help us here because, “in all reasonings from experience, there is a step taken by the mind which is not supported by any argument or process of understanding”.[xx] It is mere custom, he tells us, that drives inductive inference.

Wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding, we always say, that this propensity is the effect of Custom.[xxi]

Custom, then, is the great guide of human life. It is that principle alone which renders our experience useful to us, and makes us expect, for the future, a similar train of events with those which have appeared in the past.[xxii]

For 250 years these arguments of Hume have weathered all attempts to bring them down.[xxiii] And yet, they are flawed. Under careful analysis we find Hume not only based his critique on ill-defined premises, he also shifts frames of reference, thereby giving his arguments an impression of cogency they do not really possess. Before examining these flaws, however, it is necessary to clarify some terms.

Learning and inferring.

Learning is the psychological process of forming new ideas and new idea-relations. Learning employs a variety of methods such as insight[xxiv], trial and error[xxv], random exploration, and so forth. When a child comes to recognize his surroundings, his parents, and the family dog, he has formed new ideas. When he realizes that the family pet, Rover, the neighbor’s pet, Spot, and several other creatures resembling Rover are called dogs, he has learned to network those ideas into a specific relationship. The creating and colligating of ideas may come easily, as learning to recognize rainfall, or it may be an insight preceded by great mental effort, as Newton’s intuition that an apple and the moon are both attracted to the earth by the same force.

Inferring is not concerned with the formation of new ideas and idea-relations. Rather, (as it relates to induction) inferring is the process of expecting the facts we have already learned about the physical world to continue to hold beyond those occasions we have actually experienced. In other words, once a set of ideas and idea-relations are learned, they become the template we use for inductively inferring from the physically known to the physically unknown.

Another term having some ambiguity is inference. Normally it may be used to indicate either the process of inferring or a conclusion arrived at by inferring. I will continue to employ it in both capacities, while making an effort to keep its use contextually clear. The word induction will be used strictly to indicate a conclusion of an inductive inference.

Figure 1 schematically represents the mental operations involved in making a simple induction (admittedly, there is more going on psychologically, but the scheme is sufficient for present purposes). When the average adult looks out the window and experiences visual stimuli of water droplets falling from the sky, he instantly relates this information to his past learning and identifies (or learns) this is another instance of rain. This learned perception of “it is now raining” is immediately followed by a second process of remembering the idea-relation: “rain / has always made the ground wet”. From this past idea-relation he then infers the induction (conclusion) that “the ground will be wet”.

Seen as a sequence of logical thought, the present perception, “it is now raining” is the minor premise, the past learned idea-relation is the major premise, and the induction is the conclusion.

Although there is more to the story than Hume apparently realized, he was nonetheless correct in saying we make the kinds of inductive inference or “leap” diagrammed in Figure 1 without deliberation. That rain leads us to expect “the ground will be wet”, is the kind of automatic inference humans (and animals) make all the time. For, “the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe that it will exist”.[xxvi]

Now it is an essential part of human life to want our inductive inferences to be accurate. Indeed, it is crucial if we hope to obtain food, shelter, or avoid danger. To that end we strive to expand our learning base to as wide a premise as possible from which to make our induction. Rather than drawing our conclusion from a limited major premise, as in Figure 1, we desire to have major premises of universal scope (Figure 2). Not only is this a common and uncritical human practice, it is also one of the basic goals of philosophy, of science, and practically any systematized body of thought.

In the above diagram, the inductive “leap” is to a universal conclusion. This conclusion, coupled with the idea of rain, becomes an idea-relation that purports to cover all relevant cases - “rain will always make the ground wet”. Accordingly, this universal concept now becomes the major premise of our argument. Beginning with our minor premise (“it is now raining”) we inductively move up to the universal major premise, then by a process of deductive inference we draw the particular conclusion, “the ground will be wet”. Although this deductive conclusion is precisely the same as the conclusion arrived at inductively from the more limited major premise in Figure 1, because it is derived from a universal premise we feel it to be more secure (whether a universal premise truly is “universal” is, of course, another matter).

Historically there has been much confusion between learning and inferring.[xxvii] The creation of a new universal hypothesis or theory (as Newton’s insight regarding universal gravitation) has often been mistakenly identified as an induction similar to that diagrammed in Figure 2. But it is not. There is a critical difference. When Newton saw an apple fall to the earth, and from this he supposedly got the idea that all bodies everywhere are attracted to one another, this was not a case of inductive inference. Though he drew a universal “conclusion” from a particular perception, his insight widened the class of falling objects to include other things such as the moon and the rise and fall of the tides. This introduced new ideas and new idea-relations. Therefore, the creating of his theory was a case of learning, not inferring. Had Newton merely said, all apples that become detached from the bough will fall to the earth, that would be a universal inductive inference from his specific experience. It introduces no new ideas or new idea-relations, it merely repeats or universalizes what is already known. In the creating of his theory Newton obviously employed both learning and inferring, however, it is important to keep the distinction clear.

This confusing of learning with inferring led deductivist philosophers like Karl Popper to deny there was any place for induction in the pursuit of science.[xxviii] Though it is true, no inductive inference is used in the creating of a new hypothesis or theory, nor is it used in the deducing of a conclusion from that hypothesis, inductive inference is not to be dismissed so easily. With Newton’s theory for example, once the theory is acquired (learned) it is of little value to us unless we believe that all bodies will continue to be attracted to one another, and that expectation entails an inductive inference.

Now since all other cases of induction will fall in line if we are able to vindicate the “leap” diagrammed in Figure 1, my approach herein will be to offer a convincing justification of this simple type of inductive inference.[xxix]

As has been said, Hume rests his conclusions upon some ill-defined premises as well as shifting frames of reference. Accordingly, I will set out some fundamental categories in which to gridlock his argument.

The first categories to establish are the physical and the psychological.

The physical and the psychological.

Most adult humans recognize a difference between the physical world of objects and events, and the psychological world of ideas and feelings. Though the Berkeleian idealist might argue that everything, including the physical world, is “Ideas”, it is of no consequence here. The idealist also acknowledges that a distinction exists between what we might call the objective and the subjective – the objective being his Ideas-of-the-physical-world and the subjective being his Ideas-of-ideas, and for our purposes that distinction is sufficient.[xxx]

With regard to these two categories the question we must clarify is: Where is Hume aiming his criticism of inductive inference? Is he saying something about the physical world? Or is he saying something about the psychological? Or is he critiquing both?

The physical world

Suppose Hume is aiming his criticism at the objective world. Now when we make a statement that purports to say anything about the physical world at some future time, such as the rising of the sun tomorrow, we make an inductive inference. Such an inference could be any of the following:

1) The sun will rise tomorrow.

2) The sun will not rise tomorrow.

3) The sun may or may not rise tomorrow.

Simply put, you cannot make any prediction about the sun’s rising or not rising tomorrow, nor have any expectation about some future event (or any event not present to our senses) in the physical world, without employing an inductive inference. Nor can you make a criticism of an inductive inference without explicitly or implicitly making a counter inductive inference. In other words, when Hume says, “We cannot be sure the sun will rise tomorrow”, if he intends this criticism to have any existential significance, then he is implicitly saying something about the physical events of tomorrow. He is saying, “There is a possibility the sun may not rise tomorrow”. But that very statement is an inductive inference. He cannot escape that, because any statement which affirms or doubts the occurrence or non-occurrence of a future physical event in nature is automatically an inductive inference.

Too often the skeptical inquirer speaks as though he enjoys an unengaged position, sitting on the sidelines, suprahuman as it where, as he poses questions aimed at undermining the legitimacy of the inductive inferences of those who do science. Too often, while he judges others, the skeptic tacitly assumes that his statements and beliefs are free from any similar type judgment. But that is not so. As should be clear, Hume’s criticism (if it is meant to say anything about the physical world), implies a counter inductive inference – it posits a condition of the external world different from that which he is criticizing – and as such it places his criticism on the same plane and within the same ranks as all other inductive inferences. At which point, we are thrown back to point zero and must choose which of the competing inductive inferences is the more preferable.

To choose between competing inductive inferences, we of course need some standard of judgment on which to base our choice. What is that standard?

Of the three inductive statements above, only the first one, “the sun will rise tomorrow” originates in factual evidence. Not only are we cognizant of the stability of the planetary motions, but for countless mornings, countless people have witnessed the rising of the sun. Based upon this empirical evidence we confidently predict that “the sun will rise tomorrow”. Factual evidence, then, is the basic premise for inference (1).

What is the origin of inferences (2) and (3)? Both originate in human imagination. They refer to no precedent in physical reality.

As such, an inductive inference using a real condition of the world as its basic premise is what we deem a reasonable inference; an inductive inference using an unreal, or fanciful condition of the world as its basic premise is what we deem an unreasonable inference. “This is what “being reasonable” means in such a context.”[xxxi] If, for example, it is raining heavily and people are getting drenched as they hurry by, I can imagine that I alone will remain dry if I go out into the rain with no protection. But behavior based on such ideas is what we call unreasonable (or worse). It is unreasonable because it is behavior motivated by an inductive inference whose premises are imaginary and contrary to real factual evidence.

This is not to say that every reasonable inductive inference is valid. A reasonable or logical inductive inference is one we make based upon the factual evidence we have at our disposal when we make the inference. However, due to a lack of information, or to a modification in physical conditions, our inference may in fact turn out to be wrong, or invalid.

There are three aspects of an inductive inference that should be identified here: real, reasonable, and valid.

(i) real/unreal refers to the physical data on which an inductive inference is based. Real data is information of actual empirical things or events, whereas unreal data is inaccurate information or data that originates strictly in the human imagination. Inferences may be based either upon real or unreal data, or upon some combination of the two. (As a disclaimer here I mention the data used in such disciplines as psychotherapy. Though it may originate in the patient’s mind, yet in that context such data is empirical. Unreal data would be material the therapist creates himself and assumes is part of the patient’s worldview. However, to avoid unnecessary digression I will focus on the physical type data Hume used.)

(ii) reasonable/unreasonable refers to the psychological or mental status of the person making the inductive inference. If the inference is based upon real data then it is reasonable (or logical); if it is based upon unreal or imaginary data then the inference is unreasonable.

(iii) valid/invalid refers to the physical outcome of the inductive inference. An inference that accurately predicts or correctly corresponds to physical reality is one that is valid. If it fails to correspond to physical conditions then it is an invalid inference.

As can be seen, in Figure 4, inductive inferences such as predicting the rising of the sun are grounded (or should be grounded) in the physical world, they pass through the psychological, then conclude by being verified or falsified back in the physical world.

Inductive inferences can reflect different combinations of these three aspects. For instance, we may have had what we believed was solid evidence that a rope would hold a given weight, yet the rope broke. Since we had what we considered real data (it did not originate in our fancy) our inference was reasonable, yet it was invalid. The flaw in the sequence was that our data was in fact unreal because it did not represent the actual conditions of the rope. Still, under the circumstances the inference remains psychological reasonable. On the other hand, someone may consult an Ouija board and successfully predict where to find a lost family heirloom. In such a case we have both unreal data and an unreasonable inference, yet it turns out to be valid. This does not make the Ouija inference retroactively reasonable. Because the original data was unreal (i.e., there is no empirically verifiable link between the Ouija board and the heirloom, it was pure luck), the inference remains psychologically an unreasonable one.

Because we know Hume’s inductive inference concerning the sun not rising tomorrow is predicated upon a fantasy, we therefore know it to be unreal, unreasonable, as well as invalid the day after he made it.

In spite of Ouija boards and luck, in the long run, the optimum condition for inductive inferences is: (i) real data, (ii) a reasonable inference, and (iii) a valid outcome.

Here a skeptic might ask, but why is it preferable to chose reasonable or real-based inductive inferences? To which we reply, because in the long run reasonable, real-based inferences will tend to be more valid, and thereby deliver what we seek – knowledge and life. Whereas inaccurate or fantasy-based inferences are far more likely to bring injury and death.*

* Nelson Goodman’s “Grue” argument, and others of a similar nature, all fall by this same dictum. They employ unreal, fantasy-based inductive inferences and are thus unreasonable and almost certainly invalid.[xxxii]

As quoted above, Hume wrote, “That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise”. As others have noted, Hume’s proposition does not involve a deductive contradiction.[xxxiii] However, under prevailing conditions it is an inductive contradiction to claim that the sun will not rise tomorrow because it is an inference devoid of any real or factual foundation. Which is to say, an unreal or imagination-based inference does imply a contradiction because to be taken seriously it must posit a physical premise (e.g., planetary conditions radically altered) that is contradictory to the facts we know about the external world.

Now the skeptic may take issue with this definition of “reasonableness” because it implicitly involves the notion that nature will continue to operate in the future in much the same way as it has in the past. This assumption, it might be said, is itself an inductive inference, a case of using induction to justify induction.[xxxiv] This is true. It involves the inductive leap diagrammed in Figure 2. However, what the skeptic fails to notice is, his own negative inference suffers from a similar assumption. His unspoken major premise is that the world may suddenly be completely different. But that too, if it is to have any physical meaning, entails an inductive leap. Hence, his argument is a case of using induction to disprove induction. In short, the negative skeptical argument is of exactly the same form as the positive argument – a minor premise, a major premise concerning nature, and a conclusion concerning the sun. The difference in this specific instance is, the one inference (the positive) is founded on real factual evidence, the other inference (the negative) is based solely upon unreal (imaginary) evidence. As such, the positive inference is what we deem to be reasonable and the skeptic’s negative inference we deem unreasonable.

But what if the world should suddenly change, the skeptic asks. Does that not make our inductive inferences insecure?

To which we respond: what does “insecure” mean in this context?

Is that insecurity due to a magical view of the world or a natural view of the world? Which is to say, does the skeptic mean that inductive inferences are insecure because, by some supernatural or magical operation beyond all human expectation or comprehension, the sun might mysteriously vanish from the sky? Or does he simply mean the physical world is very complex and subject to change, and therefore natural conditions may develop (e.g., a large meteoroid may unexpectedly pass by the earth) such that for one side of our planet the sun will not rise tomorrow?

Suppose the skeptic is saying that all inductive inferences are insecure because the world is a magical, inherently unpredictable place. If so, he must also face the fact that this universal view of his, like all other claims concerning universal activities, entails an inductive inference. It involves an inductive “leap” as diagrammed in Figure 2. But from what evidence does he make this inductive “leap”? The evidence comes from his fantasy. There is no hard evidence that the world is magical or that the activity of the solar system is inherently unknowable. In light of what science tells us and all we have learned these past five hundred years any inductive conclusion that the sun might magically vanish from the sky is hardly tenable. Nor do I believe that Hume would endorse this view.

From the bulk of Hume’s writing it is safe to assume that he was suggesting something like the second of the two possibilities mentioned – the intrusion of an unforeseen natural event.[xxxv] However, if this is so, it means he tacitly endorsed the predictability of nature. That is, he believed nature operates according to specific and enduring patterns which humans are capable of sometimes understanding and using in their predictions. The drawback is, our knowledge. Our inability to be totally certain of those natural operations creates an insecurity in our inductive inferences. And it is here that the skeptical argument makes a shift in its frame of reference.[xxxvi]

Once the skeptic sees that no human can escape employing inductive inferences when referring to future (or non-present) events in the physical world, once he realizes that any serious criticism entails a counter-prediction and therefore the use of an induction, he further senses that his imagination-based inferences are obviously less tenable than factual-based inferences. At that point he shifts away from criticizing the objective physical world and slides into the realm of the subjective (psychological). His skepticism now loses its ontological focus and centers on the epistemological.

“I say nothing about whether the sun will or will not actually rise tomorrow”, he would tell us. “I am merely making a comment about human knowledge. I doubt the reliability of the inductive process because as humans we are subject to making mistakes.”

When we inquire, on what basis does he predict that humans might make a mistake, he of course points to the fact that we have made mistakes in the past: “If I am deceived once, I may all the more readily be deceived again”.[xxxvii] And, once more, as he makes this latest inductive inference, he fails to notice that he is “evidently going in a circle, and taking that for granted which is the very point in question”.[xxxviii]

The psychological

Now let us suppose the skeptic is criticizing the psychological side of inductive inference.

It is human nature to sometimes err when we make an inductive inference. Few would suggest that all our inductions are perfect. Making an error in these matters, however, in no way casts doubt upon the inductive inference process per se, any more than making a mistake in adding up a row of numbers casts doubt upon the reasoning process used in mathematics. Human errors occur with both inductive and deductive inferences, but, as I will show, these errors do not in any way invalidate the inferring process itself.

Here I wish to draw attention to a second set of categories that lie under the psychological: they are the process and content of our thought (Figure 5). In addition, two further categories are subsumed under process, they are learning and inferring, while under content are the two categories of ideas and idea-relations.

(There is considerably more going on psychologically than what is implied by this diagram, especially with regard to feelings, but for this discussion the categories shown are sufficient.)

Process and Content

The psychological process of thinking is an inborn activity. Furthermore, the thinking process called inferring is the same mental activity whether it involves deductive or inductive ideas. What differentiates the one argument from the other is the content (our ideas and the relationships of those ideas). For example, it is a deductive argument if I say:

x will always y in the morning.

It is morning.

Therefore, x will y.

On the other hand, it is an inductive argument if I say:

The sun has always risen in the morning.

It is morning.

Therefore the sun will rise.

As should be evident, it is not the mental process of passing from the first premise to the conclusion that makes these two arguments different. It is the content. It is the ideas and their relations (both what they signify and their sequence) that makes us label one a deductive argument and the other an inductive argument. In both cases it is the same inferring process, the same mental activity being used when moving from idea to idea.

As should be further evident, every inductive and deductive inference involves both a process and a content, and it is the content (ideas and idea-relations) that we judge to be valid or invalid. Sometimes our inferences are wrong, sometimes they are right. Yet, in all cases, wrong and right, deductive and inductive, we use the same process of inferring, the same mental activity.

The process of inferring, then, is a neutral activity that lies outside human judgment. It is neither right nor wrong. It is an activity that simply is. Obviously, we can neither validate nor invalidate the process we use in reasoning when we must employ that very process in arriving at our evaluation. It would only be gods or creatures outside the human species that could judge this faculty of ours.

When Hume referred to inductive inference, saying, “in all reasonings from experience, there is a step taken by the mind which is not supported by any argument or process of understanding”[xxxix], he was correct so far as the process of inferring. Our inferring process is an uncritical, reflexive action or habit. But he was not correct with regard to the other half of an inductive inference: our ideational content. Our ideas and idea-relations are not something that happen by custom or habit. On the contrary, they must be learned by experience, experience that often requires extreme mental effort.

So how, then, are inductive inferences psychologically insecure? Their insecurity lies not in the process, but in the content of our thought. Wrong ideas and wrong idea-relations cause us to make inaccurate generalizations.

Here Hume and the skeptic would exclaim, Exactly! “The course of nature may change, and the past may be no rule for the future, [thus] all experience becomes useless and can give rise to no inference or conclusion”.[xl]

To which we reply: It is not true that a change in the course of nature “can give rise to no inference”. Change may not give rise to the same inference but it surely will give rise to new inferences, inferences that accord with the new conditions. More importantly, physical change does not in any way affect the process of inferring. We use the same process of inferring whether the inference be old or new. It is the content that changes as we acquire new ideas and new idea-relations. But as has been pointed out, the acquiring of new content is learning, it is not inferring.

The fact is, we encounter change every day of our lives, and since most everyone knows it is foolish to continue basing inductive inferences on outdated content, we therefore make new inductive inferences in the face of those changes. We even understand (though hopefully the possibility is remote) that a large meteoroid could pass by and disrupt the rising of the sun tomorrow. It would be cataclysmic, but there would be nothing mystical or magical about it. Nor would it in any way threaten inductive inference as a way of dealing with the world. We would simply change our idea content and adapt our inductive inferences in accordance to the new evidence as we learn it. Under such a radical upheaval no one in his right mind would predict the usual sunrise to occur. And yet, under such horrific conditions, for someone to blithely suggest that everything would continue as normal would be an identical prediction to the fantastic prediction Hume proposed (only in reverse) - that is, currently all our evidence tells us solar and planetary conditions remain stable, yet he suggested we seriously entertain the idea that the sun might not appear tomorrow.

Causality

The relationship of cause to effect was fundamental to Hume’s view of induction. I would therefore like to examine two of his claims in that area: (1) his assertion that the relation existing between a cause and its effect “is something that exists in the mind, not in objects”[xli], and (2) it is “By means of that relation alone we can go beyond the evidence of our memory and senses”.[xlii]

(1) Cause/effect relations exist only in the mind

In Hume’s words:

When we look about us towards external objects, and consider the operation of causes, we are never able, in a single instance, to discover any power or necessary connexion; any quality, which binds the effect to the cause, and renders the one an infallible consequence of the other. We only find, that the one does actually, in fact, follow the other. The impulse of one billiard-ball is attended with motion in the second. This is the whole that appears to the outward senses.[xliii]

All events seem entirely loose and separate. One event follows another; but we never can observe any tie between them. They seem conjoined, but never connected.[xliv]

Were such a man as Adam created in the full vigor of understanding, without experience, he would never be able to infer motion in the second ball from the motion and impulse of the first.[xlv]

So where, then, is the necessary connection? Hume tells us:

… after a repetition of similar instances, the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe that it will exist. This connexion, therefore, which we feel in the mind, this customary transition of the imagination from one object to its usual attendant, is the sentiment or impression from which we form the idea of power or necessary connexion.[xlvi]

When we say, therefore, that one object is connected with another, we mean only that they have acquired a connexion in our thought.[xlvii]

Now it may be true, the first time Adam saw one billiard ball approaching another he could not infer that upon impact the first ball would set the second ball in motion. From this Hume concludes that the necessary connection must reside strictly in Adam’s mind, otherwise Adam would have been able to perceive the connection immediately.

However, it is equally true that the first time Adam saw a right-angled triangle he’d not be able to recognize that the square of the diagonal was equal to the sum of the squares of the other two sides. Does this mean that that geometric truth does not reside objectively in the triangle? Does the geometric relationship come into existence only when Adam learns of it? And if he never learns of it does it not objectively exist?

Hume was correct when he said the learning of a cause/effect relation often takes time, involves repetition, and creates a new idea-relation in our minds. He was also correct when he said, after a cause and effect relation has been learned we automatically infer the one from the other. But he was mistaken when he concluded that the acquiring of new idea-relations is all there is to causal necessity.

I contend that Hume’s descriptions of causal connections recognize only the subjective, or psychological side of things. Further, this one-sided subjective view provides no means by which to distinguish between those relations we call causal and those we call coincidence. To wit: For many years, the robins have returned in the spring and they hop across my dead and withered lawn. Shortly after the robins appear, the green grass begins to sprout. Here is a case where many primitive minds might conclude from the evidence that the robins caused the grass to grow. If this constant conjunction of robins and sprouting grass continues year after year, and if causal relations reside only in the mind of the observer, then by Hume’s formula these two events are causally connected. Yet we know they are mere coincidence. How do we persuade the person who believes the robins and the sprouting grass are joined causally to even question this mental connection, when all Hume’s criteria of causality continue to be fully met?

The truth is, there is also an objective side to causality. There is a necessary connection between a cause and its effect that exists outside the mind. When we do not perceive that connection, either directly or indirectly, we seek it out. Then, if we do not find it, we begin to suspect the events are coincidental.

Hume’s subjective one-sidedness in this matter can be traced to his static view of causality. The necessary connection of which I speak, however, is dynamic. Little wonder Hume could see no objective and necessary connection existing between a cause and its effect: the static window through which he viewed the world prevented him from seeing it. As evidence, it is enlightening to look at Hume’s statement on this (the italics in the following quotation are Hume’s, the underlining is mine):

Here is a billiard ball lying on the table, and another ball moving towards it with rapidity. They strike; and the ball, which was formerly at rest, now acquires a motion. This is as perfect an instance of the relation of cause and effect as any which we know, either by sensation or reflection. Let us therefore examine it. ‘Tis evident, that the two balls touched one another before the motion was communicated, and that there was no interval betwixt the shock and the motion. Contiguity in time and place is therefore a requisite circumstance to the operation of all causes. ‘Tis evident likewise, that the motion which was the cause, is prior to the motion which was the effect. Priority in time is therefore another requisite circumstance in every cause. But this is not all. Let us try any other balls of the same kind in a like situation, and we shall always find, that the impulse of the one produces motion in the other. Here therefore is a third circumstance, viz. that of constant conjunction betwixt the cause and effect. Every object like the cause, produces always some object like the effect. Beyond these three circumstances of contiguity, priority, and constant conjunction, I can discover nothing in this cause. [xlviii]

Though he obviously perceived motion taking place, Hume did not consider the motion to be a requisite aspect of the cause-effect relation. Living as he was in the pre-Faraday era of a mechanistic Zeitgeist, all he could “discover” was the three static conditions of contiguity, priority, and constant conjunction. Beyond these he could “discover nothing”. He thus failed to recognize that the necessary causal connection he sought was right there in front of him. But it was dynamic, and so it remained invisible to his mind set. The necessary connection he could not discover was the transference of energy from the cause to the effect. In the case of the billiard balls colliding it was the transference of motion, or kinetic energy, that linked the one to the other. This energy-link is the necessary connection that exists in all causal relations. All cause-effect events, whatever their nature, will always involve energy of some kind passing from the cause over to the effect. It is the energy-link that ties the cause to the effect. This energy-link does not exist in the case of coincidental events. Two events that are coincidental are time-linked only. They are sequential in time, but no energy (force, motion, etc) passes from the one object(s) to the other. All cause-effect events, on the other hand, are both energy-linked and time-linked.

In keeping with his static view of things Hume referred to cause and effect as objects. It would, however, be more helpful to describe these things in terms of a causal-complex and an effects-complex. In the case of his billiard ball example, the causal-complex is the moving white ball traveling toward the static red ball plus the billiard table with its level surface, felt covering, and so forth. The effects-complex is the white ball now static and the red ball in motion on the same billiard table with the same felt covering, etc. The point is, all the objects and all the energy existing in the causal-complex are still there in the effects-complex, only the configuration of objects and energy has been shifted around.

In a wider context, the universe itself, with its innumerable objects, motions, forces, and configurations is at every instant a causal-complex passing into an effects-complex, which then becomes a new causal-complex that passes into a new effects-complex, ad infinitum. Since the number of factors that can be listed in any complex are potentially limitless, we learn through science and education to limit things to what is essential for our needs. What we call “the cause” and what we call “the effect”, therefore, are dependent upon our current interests. In the above example, if the effect we are interested in is the red ball coming into motion then the moving white ball is the cause; conversely, if the effect we are interested in is the white ball coming to a halt then the static red ball is the cause. This is the reciprocity Hegel[xlix] spoke of and Newton[l] enshrined in his third law.

(2) All inductive inferences are based upon cause/effect relations:

The second of Hume’s causal claims I would briefly like to comment on is his contention that all inductive inference is based on causal connections, and it is, “By means of that relation alone we can go beyond the evidence of our memory and senses”.[li]

Though we do make inductive inferences on the basis of cause and effect, our inferences are not restricted to that relation “alone”. We also make inferences on the basis of other criteria, such as classification. When we say, all ravens seen thus far have been black, therefore, the next raven we see will probably be black, this is an inference which uses classification in its premises. It infers that the next raven will possess the attribute black because black is one of the properties belonging to members of the class of ravens. But the relationship between the color black and the class of ravens is not a cause-effect relation. Nor is black a necessary qualification of class membership; it is merely one of the many properties we list when we describe ravens. Further, because one or more of the properties belonging to an object may be altered yet the object will remain part of the classification, there is a certain insecurity involved with these types of inferences.

Nonetheless, we do make causal-based inferences, and our trust in those inferences springs from an awareness that if we can reproduce a known causal-complex we will then reproduce the expected effects-complex. Strictly speaking it is impossible to reproduce the same causal-complex down to the last configuration of atoms. However, this we have learned: when we have a causal-complex A, that has resulted in an effects-complex ß, the closer we can replicate the conditions of A the closer we will replicate the conditions of ß. This we see all about us, and it is an operative principle in all controlled experiments as well as daily life. Conversely, the less our causal-complex resembles A, the less will our effects-complex resemble ß. By a process of mental projection we then conclude that, if we could make a perfect replication of A we would get a perfect replication of ß. It is this mental ideal of a perfect replication that lies at the heart of all philosophical belief in a principle of causality.

Skepticism and Dogma

Hume consigned all metaphysical writings “to the flames”.[lii] He disliked metaphysical speculation because it was the imposing of human fantasy upon the physical reality of the world. Yet his own critique of inductive inference employs the very device he scorned. To fancy that, under normal conditions and with no factual evidence upon which to base his inference, “the sun may not rise tomorrow”, and to propose that fantasy as an actual condition of nature, is precisely the sort of sophistry and illusion he condemned. In fact, one of the glaring faults of runaway skepticism is its habitual use of the very principles it rebukes in the works and words of dogmatic thinkers.

To illustrate this let us examine Descartes” suggestion that perhaps everything we perceive in the world is an illusion. For all we know we may be under the spell of an arch deceiver,[liii] an evil genius who makes all things of the physical world appear real to us, while in fact, they are illusory. A more contemporary version is the suggestion that we may be bodiless brains in a vat of nutrients, our cerebral nerve endings wired to super computers, computers manipulated by an evil scientist who delights in deceiving us into thinking we are walking around, talking, working, socializing, and generally living out our lives.[liv] The point advanced is the same in both cases and I would like to address this skeptical notion in the form of a short dialogue.

EVERYMAN: When you say we “may” be under the spell of an arch deceiver, I take it you

mean, perhaps we are being deceived or perhaps we are not being deceived.

SKEPTIC: Yes, I only suggest the possibility. I am not claiming it to be one way or the other.

EVERYMAN: If we are not being deceived your suggestion has no significance to our lives. So let’s take the worst scenario, let’s focus on the possibility of our being deceived. Let me ask you, in your daily life do you recognize a difference between those things you perceive physically, such as your food, and those things you create as a fantasy in your own mind, say, a trip to Tahiti next year?

SKEPTIC: Yes, I recognize there is a difference.

EVERYMAN: And does your description of our being deceived by an evil genius originate in your physical perceptions? That is, have you physically witnessed anyone actually being totally deceived by such an evil genius? Or does this vision of an arch deceiver originate as a fantasy in your mind?

SKEPTIC: It originates as a fantasy. But I would not necessarily call it a fantasy for it could also be real.

EVERYMAN: Of course, if your mental creation was also real it would be more than a fantasy, and in such a case I agree we could be deceived. But I say your arch deceiver is only a fantasy with no real meaning for human life.

SKEPTIC: How can you be certain of that?

EVERYMAN: Because I too recognize the difference between my fantasies and those things I empirically perceive, and the choice you offer me is this – am I to believe in a world view whose origin is my own empirical evidence, or am I to believe in a world view whose origin is your mental fantasies? For me the real world is predicated on a lifetime of perceptual experiences, experiences that tell me that I am not under the spell of a deceiving evil genius .

SKEPTIC: You can choose as you like. But I maintain we do not know, and your world view you think is based upon empirical evidence may in fact be contained within a greater world view of deception.

EVERYMAN: And I reply just as categorically that your world view of deception is contained within my world view of perceptual evidence. For I have perceived you admit that the origin of your world view is your fantasy, while you have not perceived me being deceived by an evil genius.

SKEPTIC: Still, you must admit, we are sometimes deceived in our perceptions. We make mistakes. We suffer from illusions. How can you be sure that all our perceptions are not illusions on some higher plane.

EVERYMAN: Ah, but you confuse the occasional mistaken perception with being deceived in total. We have perceptual evidence of our mistakes, evidence you have just appealed to, but we have no evidence of our total deception. By your fantasy you presume to step outside the human condition and into a suprahuman dimension, and there you imagine you fathom a deeper and more true reality than what I perceive. Do you seriously contend that you are able to step outside the human condition and view such a realm?

SKEPTIC: No human can do that. I only suggest that maybe in a higher dimension we would be seen as dwelling in complete illusion.

EVERYMAN: But your “maybe” is a fantasy, subject neither to falsification nor verification. I therefore reject it in favor of my own perceptual evidence. Let me make this clear. We dwell and perceive the world about us in what I will call Level I, or the human level of perception. On this Level I of existence we experience both what we consider to be correct perceptions as well as errors in perception. What you have done is to take one aspect of our human experience, namely our perceptual errors, and from that partial evidence you postulate a Level II, or a suprahuman dimension where we are seen as living in total error of perception. I contend that you cannot take partial evidence from Level I and use it as the basis of conditions supposedly existing on Level II. Either your Level II worldview must be projected from all our perceptual evidence, or you must have direct evidence from Level II itself. But by your own admission no human can ever hope to experience anything on Level II. Furthermore, since you recognize that sometimes our human perceptions on Level I are mistaken, I presume you also acknowledge we have other human perceptions which we claim are not mistaken.

SKEPTIC: True, in the realm you have labeled Level I we have both what we refer to as correct perceptions as well as illusions, otherwise we could not differentiate.

EVERYMAN: So why take instances of human error to build a world view? Could we not with equal validity and with equal evidence, construct a suprahuman world view based on those occasions when we have correct perceptions? In fact, are there not some people who do just this? Are there not some who, rather than recognizing that they experience both correct as well as incorrect perceptions, focus exclusively on their ability to experience correct perceptions, and from this they create a suprahuman world view in direct opposition to yours. What is your reply to someone who claims he is infallible and that his errors of perception are not errors because on a higher suprahuman Level II, a level he conceives of in his mind, he is an infallible creature and cannot err?

SKEPTIC: I would say his view clashes with the evidence and is an illusion.

EVERYMAN: When you say “clashes with the evidence” I take it you mean it is contrary to empirical evidence on Level I, where we experience both true and false perceptions.

SKEPTIC: Precisely.

EVERYMAN: But how, in principle, does his suprahuman fantasy differ from yours? Like you, he has taken partial evidence from Level I and postulated a Level II where that partial evidence becomes a total condition. Do you not agree that both these suprahumman worldviews “clash with our perceptual evidence”?

SKEPTIC: I say there is a distinction here. His claim of infallibility is merely a personal self delusion, whereas I am postulating a possible condition of humanity itself.

EVERYMAN: This is a distinction without a difference. Indeed, there are others of his type who speak as you do and postulate their fantasy as a condition affecting all humanity. Surely you are aware of those who, from some human truth or half-truth, leap to a suprahuman Level II where no living human can enter, and from their imaginary visit to this realm these religious or metaphysical dogmatists bring us back evidence of infallible truths which we must accept on the basis of their word alone – blind faith in other words.

SKEPTIC: Everyone is aware of such views.

EVERYMAN: Well, to me the Level II world of the dogmatist and the Level II world of the skeptic are two sides of the same coin. It is inconsequential whether such a suprahuman dimension is created out of our errors or our truths, both are cut from the same imaginary cloth. The reality is: we live in a human world and it is by human standards alone that our perceptions must be judged.

SKEPTIC: But if Level II as you call it is all meaningless fantasy, what does this say about the fundamental theories of science, such as the atomic theory of matter? No one has seen an atom, yet science seriously accepts such suprahuman descriptions as valid. Are you saying these reductionist type theories are all meaningless?

EVERYMAN: No; a theory like the atomic theory need not be meaningless. Nor do such theories adopt a suprahuman point of view. Rather, they are models, humanly-created, that we use to try and explain our perceptual data on level I. Furthermore, these theories do not explicitly select some perceptions on Level I as evidence of their correctness, then claim our other perceptions don’t count. In fact, contrary perceptions on Level I can bring down a reductionist theory. The history of philosophy and science is littered with reductionist theories that have fallen because they have run up against some evidence of our senses.[lv] On the other hand, a Level II theory such as your deceiving demon lies outside all challenge from human perceptual evidence. It is a theory that dwells among the gods, or, more precisely, in your inaccessible fantasies.

SKEPTIC: So, essentially you are saying the only place where all humans can find common ground is on Level I, since that is our final source of arbitration.

EVERYMAN: Exactly. But this does not say we cannot speculate about unperceivable things. Whether we take a realist or a an instrumentalist approach we must speculate if we hope to rise above the animal level of life. The problem comes when our speculation creates an overview based upon only partial human evidence. For Empiricist thinkers this can lead to a skeptical world view, while for Rationalist thinkers it often leads to a dogmatic worldview. As humans we are all aware of experiencing a stream of what we refer to as true perceptions as well as encountering the occasional illusion, and it serves no good purpose to seize upon one type of perception to the exclusion of the other and claim that that one type is evidence of some unseen but higher and truer reality. As I have said, we live in a human world, where it is by human standards that our perceptions must be judged, and the fanciful realms of judgment that the skeptic and mystic weave are the haunts of superstition and metaphysics at its worst.

In summary

All predictions or statements about the physical world beyond our present senses, including skeptical statements about the world, employ inductive inference. Thus, when confronted by a skeptic who asks, “How can you be sure the sun will rise tomorrow?” We reply, “Because I base my inference upon the available empirical evidence, on what do you base your inference?” Should the skeptic retort, “But we have been wrong in the past.” We reply, “We have also been right in the past, so I prefer to base my inference on the factual evidence and not on your fantasies.” We define an inductive inference as reasonable when it is predicated upon real or factual evidence and as unreasonable when founded upon human fantasy or unreal evidence. Valid inductive inferences are those which accord with physical reality, and reasonable inferences are far more likely to be valid than unreasonable inferences. Further, our sciences and our experiences have taught us that the course of nature follows certain definable and predictable paths, and that causal events are both energy-linked and time-linked whereas coincidental events are time-linked only. Our philosophical conception of causality is predicated upon the observation that the closer we can duplicate a previous causal complex the closer we will duplicate the effects complex that followed from that causal complex. We also know that things are able to be classified into identifiable groups, and though there exist anomalies in most groupings we are able to make inductive inferences based upon the consistency rate of the attributes the group members possess. Too often it has been the skeptic’s assumption that his criticisms were free of those shortcomings he lays bare in dogmatic beliefs. But under closer scrutiny we find skepticism falls by its own sword – both in the making of unwarranted inductive inferences and in the postulating of a biased suprahuman point of view. It is by human standards, not suprahuman standards that our perceptions must be judged, and such standards must take into account that our experiences entail both valid and invalid perceptions. To erect a worldview that ignores half our perceptual experience is a system suffering from poverty of thought.

Looking back over the long controversy surrounding inductive inference one is reminded of the fable of the blind men and the elephant. If the question were asked, who was right and who was wrong in this controversy, the answer would be: everyone. Every argument, from Hume on down has had something legitimate to claim. Yet, because each was dwelling upon different aspects of a many-sided issue (physical v psychological, process v content, learning v inferring, inductive v deductive) they failed to address one another’s concerns. Hopefully, what has been said here will brush away the confusion and skeptical clouds that have obscured the foundations of inductive inference and help restore it to the position of glory it once held in the exuberant days of Francis Bacon.

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[i] Francis Bacon, Novum Organum, Bk. I, § 19, 40, 69, 104-6.

[ii] David Hume: An Enquiry Concerning Human Understanding, XII, Part III, § 129-130 (London: Clarendon Press, 1966), 161-162. Also, “An Abstract of a Treatise of Human Nature”, A Treatise of Human Nature, D.F. Norton, M.J. Norton (eds.) (Oxford, U.K.: Oxford University Press, 2000), 413-414.

[iii] Cf. Bertrand Russell, The Problems of Philosophy, Chap. 6 (New York: A Galaxy Book 1959), 60-69.

[iv] David Hume, An Enquiry Concerning Human Understanding, II, part 2, § 32 (London: Clarendon Press, 1966), 38

[v] Hans Reichenbach, Theory of Probability (Berkeley: University of California Press, 1971), 481. Also, C. S. Peirce, Philosophical Writings of Peirce, Justus Buchler (ed.) (New York: Dover Publications, 1955), chapters, 11, 13, 14.

[vi] For an overview of the major “solutions” to Hume’s problem: “The Justification of Induction”, Probability, Confirmation, and Simplicity, M. H. Foster and M. L. Martin (eds.) (New York: The Odyssey Press, 1966) 335-459.

[vii] The classic apriori answer to Hume’s problem was, of course, Immanuel Kant, “General Remarks on Transcendental Aesthetic”, The Critique of Pure Reason, I, §9. A different type of apriori is offered by Donald C. Williams, The Ground Of Induction (New York: Russell and Russell, 1963), 77-104. Also, Laurence BonJour, In Defense of Pure Reason: A Rationalist Account of A Priori Justification (Cambridge: Cambridge University Press, 1998), Chapter 7.

[viii] Colin Howson, Hume’s Problem: Induction and Justification of Belief (Oxford: Clarendon Press, 2000), 110.

[ix] Max Black, Models and Metaphors, Chapter 12 (Ithaca, New York: Cornell University Press, 1962), 209-218.

[x] Ian Hacking, An Introduction To Probability and Inductive Logic, Chaps. 21, 22 (Cambridge: Cambridge University Press, 2001), 252.

[xi] Stephen F. Barker, “Is There A Problem Of Induction?”, The Justification of Induction, Richard Swinburne (ed.) (London: Oxford University Press, 1974), 59.

[xii] Alfred Jules Ayer, Language, Truth and Logic, (New York: Dover Publications, 1952), 50.

[xiii] C.D. Broad, The Philosophy of Francis Bacon (New York: Octagon Books, 1974), 67.

[xiv] David Hume, An Enquiry Concerning Human Understanding, IV, Part I, § 20-21 (London: Clarendon Press 1966), 25-26.

[xv] John Stuart Mill, A System of Logic, III, Ch. 3 §1, (London: Longman, 1970), 201. Mill was very aware that his belief in the uniformity of nature and in universal cause and effect were, themselves, inductive inferences. Pp. 203, 371.

[xvi] David Hume, An Enquiry Concerning Human Understanding, IV, Part II, § 32 (London: Clarendon Press, 1966), 37-38.

[xvii] Richard von Mises, Positivism (Cambridge, USA: Harvard University Press, 1951), 163-164. Also Hans Reichenbach, The Theory of Probability, (Berkeley, USA: University of California Press, 1971), 429.

[xviii] J. M. Keynes, A Treatise on Probability (Macmillan and Co.: London), 1921, 4. Also, Rudolf Carnap, Philosophy of Science, 12, no. 2 (1945), 72-97.

[xix] David Hume, An Enquiry Concerning Human Understanding, IV, Part II, § 30 (London: Clarendon Press, 1966), 35-36.

[xx] David Hume, An Enquiry Concerning Human Understanding, V, Part I, § 34 (London: Clarendon Press, 1966), 41.

[xxi] David Hume, An Enquiry Concerning Human Understanding, V, Part I, § 36 (London: Clarendon Press, 1966), 43.

[xxii] David Hume, An Enquiry Concerning Human Understanding, V, Part I, § 36 (London: Clarendon Press, 1966), 44.

[xxiii] Cf. Colin Howson, Hume’s Problem: Induction and Justification of Belief, (Oxford: Clarendon Press, 2000), 109.

[xxiv] Wolfgang Kohler, The Mentality of Apes, (New York: Vintage Books, 1956), p. 31.

[xxv] Edward L. Thorndike, see Theories of Learning, Chapter 2, E.R. Hilgard (New York: Apple-Century Crofts, 1956), pp. 15-17.

[xxvi] David Hume, An Enquiry Concerning Human Understanding, VIII, § 59 (London: Clarendon Press, 1966), 75.

[xxvii] The distinction between learning and inferring has been made many times: e.g., Carl G. Hempel, “Recent Problems of Induction”, in Mind and Cosmos, ed. Robert G. Colodny (University of Pittsburgh Press: Pittsburgh, USA, 1966), 113-117. The debate between John S. Mill and William Whewell involved a difference of opinion on this point. John S. Mill, A System of Logic, Bk. III, Chap. II, §3-4-5, (London: Longman, 1970), 191-200. William Whewell, On The Philosophy of Discovery Chap.22, §2-3, (New York: Burt Franklin, 1971), 247-262, esp. 254.

[xxviii] Cf. Karl Popper, The Logic of Scientific Discovery, appendix I, 2 (Toronto: University of Toronto Press, 1959), 27-29, 315.

[xxix] As Hume put it, “If we can explain the inference from the shock of two balls, we shall be able to account for this operation of the mind in all instances”. “An Abstract of a Treatise of Human Nature”, A Treatise of Human Nature ed. D.F. Norton, M.J. Norton (eds.) (Oxford, UK: Oxford University Press, 2000), 410. Also, Wesley C. Salmon, “The Foundations of Scientific Inference”, Mind and Cosmos, Robert G. Colodny (ed.) (Pittsburgh: University of Pittsburgh Press, 1966), 154.

[xxx] “The ideas imprinted on the Senses by the Author of nature are called real things [objective], and those excited in the imagination being less regular, vivid, and constant, are more properly termed ideas, or images of things [subjective]…It will be objected that by the foregoing principles all that is real and substantial in nature is banished out of the world, and instead thereof a chimerical scheme of ideas takes place… What therefore becomes of the sun, moon, and stars…Are all these but so many chimeras and illusions of the fancy? To all which, and whatever else of the same sort may be objected, I answer, that by the principles premised we are not deprived of any one thing in nature. Whatever we see, feel, hear… is as real as ever. There is a rerum natura, and the distinction between realities and chimeras retains its full force… but then they both equally exist in the mind, and in that sense they are alike ideas.” George Berkeley, “A Treatise Concerning The Principles of Human Knowledge”, § 33, 34, Great Books of the Western World, 35 (Chicago, USA: Encyclopedia Britannica, 1952), 419.

[xxxi] Peter Strawson, Introduction To Logical Theory, (Chap. 9) (New York: John Wiley and Sons, 1953), 257. From a practical point of view, I suspect Hume would not argue with this definition of inductive reasonableness: “A wise man, therefore, proportions his belief to the evidence”. David Hume, An Enquiry Concerning Human Understanding, X, § 87 (London: Clarendon Press, 1966), 110.

[xxxii] Nelson Goodman, Fact, Fiction and Forecast (New York: Bobbs Merrill Co., 1965), 73-74.

[xxxiii] Cf. Wesley C. Salmon, “Symposium on Inductive Evidence”, The Justification of Induction, Richard Swinburne (ed.) (London: Oxford University Press, 1974),48.

[xxxiv] David Hume, An Enquiry Concerning Human Understanding, IV, Part II, § 30 (London: Clarendon Press, 1966), 35-36.

[xxxv] Cf. David Hume, “Of Miracles”, An Enquiry Concerning Human Understanding, X, (Clarendon Press: London, 1966).

[xxxvi] There is no one critical point where Hume overtly makes this frame of reference switch, rather, he generally runs the physical and the psychological dimensions together often making it unclear as to which he is referring.

[xxxvii] George Santayana, Scepticism and Animal Faith, (London: Constable and Co., 1924), 115.

[xxxviii] David Hume, An Enquiry Concerning Human Understanding, IV, Part II, § 30 (London: Clarendon Press, 1966), 35-36.

[xxxix] David Hume, An Enquiry Concerning Human Understanding, V, Part I, § 34 (London: Clarendon Press, 1966), 41.

[xl] David Hume, An Enquiry Concerning Human Understanding, IV, Part II, § 32 (London: Clarendon Press, 1966), 37-38.

[xli] David Hume, A Treatise of Human Nature, Vol I, Part 3, Sect. 14 (London: J. M. Dent & Sons, 1959), 163.

[xlii] David Hume, An Enquiry Concerning Human Understanding, I, Part IV, § 22 (London: Clarendon Press, 1966), 26.

[xliii] David Hume, An Enquiry Concerning Human Understanding, VII, Part I, § 50 (London: Clarendon Press, 1966), 63.

[xliv] David Hume, An Enquiry Concerning Human Understanding, VII, Part II, § 58 (London: Clarendon Press, 1966), 74.

[xlv] David Hume, “An Abstract of a Treatise of Human Nature”, A Treatise of Human Nature ed. D.F. Norton, M.J. Norton (eds.) (Oxford, UK: Oxford University Press, 2000), 410.

[xlvi] David Hume, An Enquiry Concerning Human Understanding, VII, Part II, § 59 (London: Clarendon Press, 1966), 75.

[xlvii] David Hume, An Enquiry Concerning Human Understanding, VII, Part II, § 60 (London: Clarendon Press, 1966), 76.

[xlviii] David Hume, “An Abstract of a Treatise of Human Nature”, A Treatise of Human Nature ed. D.F. Norton, M.J. Norton (eds,) (Oxford, UK: Oxford University Press, 2000), 409.

[xlix] G.W.F. Hegel, Logic §154-7 (London: Oxford University Press, 1975), 217-219.

[l] Isaac Newton, “Mathematical Principles of Natural Philosophy”, Great Books of the Western World, Vol. 34 (Chicago, USA: Encyclopedia Britannica, 1952), 14.

[li] David Hume, An Enquiry Concerning Human Understanding, I, Part IV, § 22 (London: Clarendon Press, 1966), 26.

[lii] David Hume, An Enquiry Concerning Human Understanding, XII, Part III, § 132 (London: Clarendon Press, 1966), 165.

[liii] Rene Descartes, “Meditations I”, Great Books of the Western World, Vol.. 31 (Chicago, USA: Encyclopedia Britannica, 1952), 77. Also David Hume, An Enquiry Concerning Human Understanding, XII, Part I, § 119 (London: Clarendon Press, 1966), 153.

[liv] Hilary Putnam, “Brains In A Vat”, Skepticism, A Contemporary Reader, Keith DeRose, Ted A. Warfield (eds.) (New York: Oxford University Press, 1999), 30.

[lv] Cf. Cecil J. Schneer, “The Composition of Things”, The Evolution of Physical Science, chap. 9 (New York: Grove Press, 1960 )131-158. Also, Early Greek Philosophy, Milton C. Nahm (New York: Appleton-Century-Crofts, 1964), 3-4

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Inductive

‘leap’

Inferring

Learned idea-relations

It is now raining

Rain has always made the ground wet.

Deductive inference

Inductive ‘leap’

(Rain) WILL ALWAYS make the ground wet.

UNIVERSAL conclusion

Learned idea

Impressions

Perception

Visual stimuli

Rain

Particular conclusion

Learning

[Figure 2]

‘the ground will be wet’

[Figure 4]

[Figure 3]

Learning | Inferring

[Figure 5]

Ideas | Idea-relations

Process Content

Objective Subjective

Physical World Psychological

Physical status of the conclusion of an Inductive Inference

Learned ideas

Objective Subjective

Physical World Psychological

VALID / INVALID

Deduction

Impressions

REASONABLE / UNREASONABLE

Psychological status of an Inductive Inference

Physical status of data on which Inductive Inference is based

Objective Subjective

Physical World Psychological

REAL / UNREAL

Perception

Visual stimuli

Past perceptions of Rain

[Figure 1]

It is now raining

‘the ground will be wet’

Induction

Learned idea-relations

Rain has always made the ground wet.

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